Terry Tao has a very fine thread on Collaboration in his blog.
Coincidently, I just quoted him on the n-Category Cafe blog on the
recurring seqfans topic of open source mathematics and what makes a
sequence beautiful:
==============
<a href="http://golem.ph.utexas.edu/category/2009/02/last_person_standing.html">Last
Person Standing
Posted by David Corfield</a>
Tim Gowers is engaged in a new venture in open source mathematics. As
one might expect from a leading representative of the
'problem-solving' culture, Gowers has proposed a blog-based group
problem solving challenge.
He motivates his choice of problem thus:
Does the problem split naturally into subtasks? That is, is it
parallelizable? I'm actually not completely sure that that's what I'm
aiming for. A massively parallelizable project would be something more
like the classification of finite simple groups, where one or two
people directed the project and parcelled out lots of different tasks
to lots of different people, who go off and work individually. But I'm
interested in the question of whether it is possible for lots of
people to solve one single problem rather than lots of people to solve
one problem each. [truncated]
==============
Tao on Lax as Miraculous; Re: Last Person Standing
In Bulletin of the AMS, Vol.46, No.1, Jan 2009, p.10, of Terry Taos's
wonderful survey "Why Are Solitons Stable?" he says of the inverse
scattering approach:
"This is a vast subject that can be viewed from many different
algebraic and geometric perspectives; we shall content ourselves with
describing the approach based on Lax pairs, which has the advantage of
simplicity, provided that one is willing to accept a rather miraculous
algebraic identity…."
So, beauty from something that looks at first like a weird
coincidence, which on further analysis is so deep that it appears a
miracle, even to a genius such as Tao!
Surely this matters very much, both in the Physics and the Mathematics
perpectives.
On Thu, Feb 19, 2009 at 9:59 AM, Alexander Povolotsky
<apovolot at gmail.com> wrote:
> FYI - Terence Tao's remark, mentioning OEIS (I made it bold)
>> ARP
> =========================================================================
>http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/> February 1, 2009 at 8:27 pm
> I can't speak for others, but as for my own research, at least half of my
> papers are joint with one or more authors, and amongst those papers that I
> consider among my best work, they are virtually all joint.
> Of course, each mathematician has his or her own unique research style, and
> this diversity is a very healthy thing for mathematics as a whole. But I
> think 21st century mathematics differs from 19th and early 20th century
> mathematics in at least two important respects. Firstly, the advent of
> modern communication technologies, most notably the internet, has made it
> significantly easier to collaborate with other mathematicians who are not at
> the same physical location. (Most of my collaborations, for instance, would
> be non-existent, or at least significantly less productive, without the
> internet.) One can imagine the next generation of technologies having an
> even stronger impact in this direction (with this project possibly being an
> example; other extant examples include Wikipedia and the *Online
> Encyclopedia of Integer Sequences*).
> ...
> =====================================================================
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